What is the value of the leading coefficient a, if the polynomial function P(x) = a(x + b)2(x − c) has a multiplicity of 2 at the point (−1, 0) and also passes through the points (7, 0) and (0, −14)?

A:2

B:-2

C:7

D:-14

Thanks for the help :)

Guest Mar 13, 2018

#1**+1 **

If we have a multiplicity of 2 at (-1,0) and the point (7,0) is also on the graph, we must have that

P(x) =

a (x + 1)^2 (x - 7)

a (x^2 + 2x + 1) (x - 7)

a(x^3 + 2x^2 + x -7x^2 -14x - 7)

a(x^3 - 5x^2 - 13x - 7)

And if (0, -14) is on the graph.....we have that

-14 = a ( 0^3 - 5(0)^2 - 13(0) - 7)

-14 = -7a

a = 2

Here's a graph : https://www.desmos.com/calculator/wbejrdzi2x

CPhill
Mar 13, 2018